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Table 7 Numerical equation of the heat transfer model

From: Optimization of PC micro-drilling using a continuous CO2 laser: an experimental and theoretical comparative study

Boundary condition

Equation

Description

Equation parameters

Governing equation

\(\rho {C}_p\frac{\partial T}{\partial t}=K{\nabla}^2T+Q\)

The partial differential eq. of heat conduction through the material

ρ: the specimen’s density (kg cm−3)

Cp: the specific heat (J kg−1 K−1)

k: The thermal conductivity (Wm−1K−1)

Q: represents a distributed heat generation term

T: represents the temperature field as a function of time and space (K)

Conduction heat flux

\(hf=\frac{P}{\pi {r}_b^2}\ {e}^{\frac{-2{r}^2}{r_b^2}}\)

The heat flux occurs on the sample’s top surface

hf: laser heat flux (Wm−2)

P: laser power (W)

rb: radius of the laser spot at the workpiece’s surface (μm)

r:the radial distances from the center of the laser beam point

Convection heat flux

Qc = Ashc(T − Tamb)

The heat flux occurs at the sample’s boundary

Qc: convective heat flux (W/m−2)

hc: coefficient of convective heat transfer (W/m−2 K−1)

T: specimen temperature (K)

Tamb: ambient temperature (K)

Radiation heat flux

\({Q}_r={A}_s\varepsilon \sigma \left({T}^4-{T}_{\textrm{amb}}^4\right)\)

ɛ: the material emissivity

𝛔: Stefan–Boltzmann constant (Wm−2 K4)